Delaunay triangulation is one of the central topics in mesh generation due to its theoretical properties that have been well-studied in 2D space [1]}, [2]} and can be extended to 3D or even higher. In this section, we mainly focus on Delaunay tetrahedral partition in the 3D Euclidean space. Given a set of vertices \(\mathcal {V}\) , a tetrahedral partition \(\triangle \)  is called Delaunay tetrahedral partition if for every tetrahedron \(T\)  in \(\triangle \) , there is no vertex \(v \in \mathcal {V}\)  lying in the interior of the ball passing through the vertices of \(T\) . The 3D Delaunay tetrahedral partition maximizes the minimal solid angle appearing in the tetrahedra in \(\triangle \) . Chapter 16 in [3]} provides a detailed discussion of various theoretical properties for tetrahedral partitions.
<FIGURE>